SIAM 2023 Schedule

This talk will address the design of an implantable bioartificial pancreas without the need for immunosuppressant therapy. The design is based on transplanting the healthy (donor) pancreatic cells into a poroelas- tic medium (alginate hydrogel, or agarose gel) and encapsulating the cell-containing medium between two nanopore semi-permeable membranes. The nanopore membranes are manufactured to block the immune cells from attacking the organ, while allowing passage of nu- trients and oxygen to keep the transplanted cells viable as long as possible. The key challenge is main- taining the survival of transplanted pancreatic cells for an extended period of time by providing suffi- cient oxygen supply. This challenge is addressed via our nonlinear, multi-scale, multi-physics math- ematical and computational models. At the macro scale we designed a nonlinear fluid-poroelastic structure interaction model to study the flow of blood in the bioartificial pancreas, coupled to a non- linear advection-reaction-diffusion model to study oxygen supply to the cells. At the micro-scale, we use particle-based simulations (Smoothed Particle Hydrodynamics) in conjunction with Encoder- Decoder Convolution Neural Networks to capture the fine micro-structure (architecture) of hydrogels and how the architecture influences the macro-scale parameters, such as the spatially dependent permeability tensor. These models inspired the design of a second-generation bioartificial pancreas. They also initiated the development of new mathematical analysis approaches to study multi-layered poroelastic media interacting with incompressible, viscous fluids. I will talk about both. In particu- lar, a new mathematical well-posedness result for a nonlinearly coupled model will be shown. Parts of this work are joint with biomedical engineer S. Roy (UCSF), and mathematicians Y. Wang (Texas Tech), J. Webster (University of Maryland Baltimore County), L. Bociu (North Carolina State Univer- sity), and B. Muha (University of Zagreb, Croatia).

In biomechanics, local phenomena, such as tissue perfusion, are strictly related to the global features of the whole blood circulation. We pro- pose a heterogeneous model where a local, accurate, 3D description of tissue perfusion by means of poroelastic equations is coupled with a systemic 0D lumped model of the remainder of the circula- tion. This represents a multiscale strategy, which couples an initial boundary value problem to be used in a specific tissue region with an initial value problem in the rest of the circulatory system. We discuss wellposedness analysis for this multiscale model, as well as solution methods focused on a detailed comparison between functional iterations and an energy-based operator splitting method and how they handle the interface conditions.